from SimPEG import Maps, Survey, Utils, np, sp
from scipy.constants import mu_0
from EM1DAnal import ColeCole
from DigFilter import transFilt, transFiltImpulse, transFiltInterp, transFiltImpulseInterp
from Waveform import CausalConv
from scipy.interpolate import interp1d
class BaseEMSurvey(object):
"""docstring for BaseEMSurvey"""
def __init__(self, **kwargs):
Survey.BaseSurvey.__init__(self, **kwargs)
@property
def Qcc(self):
if getInterpolationMatttr(self, '_Qcc', None) is None:
self._Qcc = self.prob.mesh.getInterpolationMat(self.loc,'CC')
return self._Qcc
[docs]class BaseEM1DSurvey(Survey.BaseSurvey):
"""
Base EM1D Survey
"""
rxLoc = None # [xr1, yr1, zr1]
txLoc = None # [xt1, yt1, zt1]
rxType = None # Bz, dBzdt
txType = None # VMD, CircularLoop
offset = None # Tx <-----> Rx
fieldtype = None #: total or secondary fields
depth = None
topo = None
LocSigZ = None
h = None #: Tx heights at local coordinate
nlay = None #: The # of layer (fixed for all soundings)
z = None #: Rx heights at local coordinate
I = 1. #: Tx loop current
a = None #: Tx loop radius
HalfSwitch = False
def __init__(self, **kwargs):
Survey.BaseSurvey.__init__(self, **kwargs)
def Setup1Dsystem(self):
if self.HalfSwitch == False:
self.nlay = self.depth.size
elif self.HalfSwitch == True:
self.nlay = 1
else:
raise Exception('Not implemnted!!')
self.h = self.txLoc[2]-self.topo[2]
self.z = self.rxLoc[2]-self.topo[2]
@Utils.requires('prob')
[docs] def dpred(self, m, u=None):
"""
dpred(m, u=None)
Create the projected data from a model.
The field, u, (if provided) will be used for the predicted data
instead of recalculating the fields (which may be expensive!).
.. math::
d_\\text{pred} = P(u(m))
Where P is a projection of the fields onto the data space.
"""
if u is None: u = self.prob.fields(m)
if self.prob.jacSwitch == True:
u = u[0]
else:
u = u
return Utils.mkvc(self.projectFields(u))
[docs]class EM1DSurveyTD(BaseEM1DSurvey):
"""docstring for EM1DSurveyTD"""
time = None
Nch = None
Nfreq = None
frequency = None
omega_int = None
switchFDTD = 'TD'
switchInterp = False
waveType = 'stepoff'
waveform = None
waveformDeriv = None
tb = None
tconv = None
hp = None
# 1. general
# 2. stepoff
def __init__(self, **kwargs):
BaseEM1DSurvey.__init__(self, **kwargs)
def setFrequency(self, time=np.logspace(-7, -1, 256)):
self.Nch = self.time.size
wt = np.array([7.214369775966785e-20, 5.997984537445829e-20, 1.383536819510307e-20, 6.127201193993877e-20, 2.735622069700930e-20, 6.567948836420383e-20, 4.144963335850363e-20, 7.316414067200350e-20, 5.682375914662966e-20, 8.391977074915078e-20, 7.418756524583309e-20, 9.829637687190485e-20, 9.430643800653847e-20, 1.168146262188112e-19, 1.180370735968097e-19, 1.401723019040171e-19, 1.463726071463266e-19, 1.692722072070252e-19, 1.804796158499069e-19, 2.052560499147526e-19, 2.217507732438609e-19, 2.495469564846162e-19, 2.718603842873614e-19, 3.039069705922034e-19, 3.328334008394297e-19, 3.705052796297763e-19, 4.071277819975917e-19, 4.520053409594589e-19, 4.977334107366132e-19, 5.516707191291291e-19, 6.082931168675559e-19, 6.734956703766505e-19, 7.432489554623685e-19, 8.223651399147256e-19, 9.080210233648037e-19, 1.004250388267800e-18, 1.109225156214032e-18, 1.226448534750949e-18, 1.354938655056596e-18, 1.497875155579711e-18, 1.655024636692164e-18, 1.829422009902478e-18, 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ab = 0.7866057737580476e0
#------- Compute Frequency components reqired for transform -------#
# This is for Digital filtering and here we evalute frequency domain responses
# ritght at this bases.
# a. Generate time base
n = np.ceil(-10*np.log(time.min()/time.max()))
tbase = time.max()*np.exp(-0.1*np.arange(0, n+1))
self.wt = wt
self.ab = ab
self.n = n
self.tbase = tbase
# b. Determine required frequencies
omega_int = (ab/tbase[0])*np.exp(0.1*(np.r_[1:786+tbase.size:(786+tbase.size)*1j]-425))
# Case1: Compute frequency domain reponses right at filter coefficient values
if self.switchInterp == False:
self.frequency = omega_int/(2*np.pi)
self.Nfreq = self.frequency.size
# Case2: Compute frequency domain reponses in logarithmic then intepolate
elif self.switchInterp == True:
# This is tested decision: works well 1e-4-1e0 S/m
self.frequency = np.logspace(-3, 8, 81)
self.omega_int = omega_int
self.Nfreq = self.frequency.size
else:
raise Exception('Not implemented!!')
[docs] def projectFields(self, u):
"""
Transform frequency domain responses to time domain responses
"""
# Case1: Compute frequency domain reponses right at filter coefficient values
if self.switchInterp == False:
# Tx waveform: Step-off
if self.waveType == 'stepoff':
if self.rxType == 'Bz':
# Compute EM responses
if u.size == self.Nfreq:
resp, f0 = transFilt(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i], f0 = transFilt(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.time)
elif self.rxType == 'dBzdt':
# Compute EM responses
if u.size == self.Nfreq:
resp = -transFiltImpulse(u, self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i] = -transFiltImpulse(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Tx waveform: General (it can be any waveform)
# We evaluate this with time convolution
elif self.waveType == 'general':
# Compute EM responses
if u.size == self.Nfreq:
# TODO: write small code which compute f at t = 0
f, f0 = transFilt(Utils.mkvc(u), self.wt, self.tbase, self.frequency*2*np.pi, self.tconv)
fDeriv = -transFiltImpulse(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp = respint(self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
f, f0 = transFilt(u[:,i], self.wt, self.tbase, self.frequency*2*np.pi, self.tconv)
fDeriv = -transFiltImpulse(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp[:,i] = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp[:,i] = respint(self.time)
# Case2: Compute frequency domain reponses in logarithmic then intepolate
if self.switchInterp == True:
# Tx waveform: Step-off
if self.waveType == 'stepoff':
if self.rxType == 'Bz':
# Compute EM responses
if u.size == self.Nfreq:
resp, f0 = transFiltInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i], f0 = transFiltInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
elif self.rxType == 'dBzdt':
# Compute EM responses
if u.size == self.Nfreq:
resp = -transFiltImpulseInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i] = -transFiltImpulseInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Tx waveform: General (it can be any waveform)
# We evaluate this with time convolution
elif self.waveType == 'general':
# Compute EM responses
if u.size == self.Nfreq:
# TODO: write small code which compute f at t = 0
f, f0 = transFiltInterp(Utils.mkvc(u), self.wt, self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
fDeriv = -transFiltImpulseInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp = respint(self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
f, f0 = transFiltInterp(u[:,i], self.wt, self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
fDeriv = -transFiltImpulseInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp[:,i] = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp[:,i] = respint(self.time)
return mu_0*resp
[docs]class EM1DSurveyFD(BaseEM1DSurvey):
"""docstring for EM1DSurveyFD"""
Nfreq = None
frequency = None
switchRI = 'all'
switchFDTD = 'FD'
def __init__(self, **kwargs):
BaseEM1DSurvey.__init__(self, **kwargs)
[docs] def projectFields(self, u):
"""
Decompose frequency domain EM responses as real and imaginary
components
"""
ureal = (u.real).copy()
uimag = (u.imag).copy()
if self.rxType == 'Hz':
if self.switchRI == 'all':
ureal = (u.real).copy()
uimag = (u.imag).copy()
if ureal.ndim == 1 or 0:
resp = np.r_[ureal, uimag]
elif ureal.ndim ==2:
resp = np.vstack((ureal, uimag))
else:
raise Exception('Not implemented!!')
elif self.switchRI == 'Real':
resp = (u.real).copy()
elif self.switchRI == 'Imag':
resp = (u.imag).copy()
else:
raise Exception('Not implemented')
else:
raise Exception('Not implemnted!!')
return mu_0*resp
class BaseEM1DMap(Maps.IdentityMap):
"""BaseEM1DMap"""
def __init__(self, mesh, **kwargs):
Maps.IdentityMap.__init__(self, mesh)
def transform(self, m):
"""
"""
return np.exp(m)
#TODO: Need to think about this ...
def transformDeriv(self, m):
return Utils.sdiag(np.exp(m))
class BaseColeColeMap(BaseEM1DMap):
"""BaseColeColeMap"""
def __init__(self, mesh, **kwargs):
Maps.IdentityMap.__init__(self, mesh)
self.tau = kwargs['tau']
self.eta = kwargs['eta']
self.c = kwargs['c']
self.frequency = kwargs['Frequency']
def transform(self, m):
"""
Here m is going to be Nsd (The number of sounding) lists.
"""
self.frequency
sigmaCole = ColeCole(self.frequency, m, self.eta, self.tau, self.c)
return sigmaCole